# The Temporal Morphology of Infrasound Propagation

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## Abstract

Expert knowledge suggests that the performance of automated infrasound event association and source location algorithms could be greatly improved by the ability to continually update station travel-time curves to properly account for the hourly, daily, and seasonal changes of the atmospheric state. With the goal of reducing false alarm rates and improving network detection capability we endeavor to develop, validate, and integrate this capability into infrasound processing operations at the International Data Centre of the Comprehensive Nuclear Test-Ban Treaty Organization. Numerous studies have demonstrated that incorporation of hybrid ground-to-space (G2S) enviromental specifications in numerical calculations of infrasound signal travel time and azimuth deviation yields significantly improved results over that of climatological atmospheric specifications, specifically for tropospheric and stratospheric modes. A robust infrastructure currently exists to generate hybrid G2S vector spherical harmonic coefficients, based on existing operational and emperical models on a real-time basis (every 3- to 6-hours) (Drob *et al.,* 2003). Thus the next requirement in this endeavor is to refine numerical procedures to calculate infrasound propagation characteristics for robust automatic infrasound arrival identification and network detection, location, and characterization algorithms. We present results from a new code that integrates the local (range-independent) τp ray equations to provide travel time, range, turning point, and azimuth deviation for any location on the globe given a G2S vector spherical harmonic coefficient set. The code employs an accurate numerical technique capable of handling square-root singularities. We investigate the seasonal variability of propagation characteristics over a five-year time series for two different stations within the International Monitoring System with the aim of understanding the capabilities of current working knowledge of the atmosphere and infrasound propagation models. The statistical behaviors or occurrence frequency of various propagation configurations are discussed. Representative examples of some of these propagation configuration states are also shown.

### Keywords

Infrasound atmospheric variability climatology automated event detection source location CTBTO IDC IMS## 1 Background

The purpose of the automated infrasound processing developed at the IDC is to detect coherent signals measured on individual IMS sensors (Christie *et al.,* 2001), highlight the most significant detections as “phases” (as opposed to “noise”), and subsequently group these phases to form and locate hypocenters, so-called “events”. The phases are determined using the progressive multi-channel correlation (PMCC) method (Cansi, 1995) which distinguishes the coherent signals produced by natural and man-made sources from incoherent ambient background noise which may also be of natural, cultural, or instrumental origin. A wide variety of sources are regularly recorded worldwide by the IMS network; ocean activity, mountain associated waves, volcanic eruptions, earthquakes, thunderstorms, meteors, avalanches, auroras, rocket launches and re-entries, aircraft, mine-blasts, accidental explosions, and industrial noise. It is important for the IDC to detect, locate, and categorize these sources to contrast with nuclear explosions; the task of the organization.

The detection, location, and characterization algorithms (henceforth DLC) described by Brown *et al.*, (2002a) may be used to locate the terminal burst point of exploding meteors, the origin time of volcanic eruptions, and the location of avalanches and rock slides, as well other null sources relevant to CTBTO operations (Le Pichon *et al.*, 2008b; Hedlin *et al.*, 2002). Although the various natural events represent false alarms for the CTBTO, they also provide valuable ground-truth information that can be used to constantly fine-tune and check the integrity of the system, insuring verifiability of the treaty. For example, terminal bursts of meteors with an average yield of one kiloton occur in the earth’s atmosphere several times per year (Nemtchinov *et al.*, 1997; Brown *et al.,* 2002b).

To facilitate rapid computation, today’s automated DLC algorithms rely upon precompiled station travel-time information (Brown *et al.,* 2002a). The precompiled information, which is typically average propagation velocity and azimuth deviation, describes how an observed signal was affected by the background environment on its way from source to receiver. The application of this knowledge provides improved source location and signal association estimates.

Our objective is to reduce IDC false alarm rates and improve detection capability by reducing the sources of uncertainty in the existing model physics and DLC methodologies. Analyses of ground-truth events have shown that observationally constrained atmospheric specifications are superior to average climatology (Le Pichon *et al.,* 2002, 2005; Herrin *et al.,* 2006). This is particularly true for tropospheric and stratospheric propagation for which there are several global operational numerical weather prediction systems such as the NOAA Global Forecast System (Kalnay *et al.,* 1990) and ECMWF (Courtier *et al.,* 1998; Bechtold *et al.,* 2008). Unfortunately, these systems are currently limited in their altitude extent due to the unavailability of routine operational satellite observations above approximately 80 km. The ground-to-space (G2S) environmental specification system was therefore developed to provide a compact numerical weather prediction post-processor and infrasound propagation calculation preprocessor (Drob *et al.,* 2003) to account for all altitudes pertinent to infrasound propagation. The system serves as a placeholder until operational numerical weather prediction models and data sets include the lower thermosphere.

In addition to requiring up-to-date knowledge about the atmospheric state for improving DLC algorithms, an acoustic wave propagation model is required to compute how observed infrasound signals relate back to their source. In discrete inverse theory (Menke, 1989) this is known as a forward model. There are a number of propagation modeling techniques available such as ray tracing (Gossard and Hooke, 1975), parabolic equations (Lingevitch *et al.,* 2002), and normal modes (Pierce, 1967). Unfortunately with detailed physics comes greater complexity. The approach must not be so primitive that any value added from near-real-time atmospheric specification has no meaningful influence; in turn, the technique must not be so complicated that implementation is impractical in automated DLC algorithms. The data and procedures must be readily available and simple enough to integrate into operational monitoring systems.

## 2 The τp Equations

*et al.,*(1998) provide a good balance of simplicity and geophysical information content for automated DLC algorithms, particularly in conjunction with near-real-time atmospheric specifications. In general, the acoustic ray-tracing approach represents the propagation or translation and rotation of an acoustic wavefront through space and time. The τp equations are an expression of the Eikonal ray-tracing equations (Lighthill, 1978; Gossard and Hooke, 1975) in integral form with the approximations of range independence and no vertical wind. For this, each ray or wavefront element can be uniquely represented by an invariant ray parameter (

*p*),

*c*

_{ o }), the vertical wave number

*k*

_{ z }= sin(

*q*) where

*q*is elevation angle, and

*u*

_{ o }the horizontal wind velocity along the direction of propagation at the receiver. This ray parameter is also the reciprocal of the intrinsic horizontal phase velocity of the wave

*V*

_{θ}= 1/

*p*, therefore;

*z*

_{ o }is the lower limit of integration (typically zero or the surface altitude) and

*z*(

*p*) is the upper limit, which is the first root above

*z*

_{ o }of the characteristic function.

*V*

_{θ}) matches that of the background effective sound speed,

*c*(

*z*) +

*u*(

*z*) where these are the adiabatic sound velocity and horizontal wind speed along the direction of propagation, respectively. The infrasound propagation characteristics in Eqs. 3 and 4 are a function of the local vertical profiles of

*ζ*(

*z*) = 1/

*c*

^{2}(

*z*) and

*u*(

*z*) as well. The corresponding travel time (

*T*) for a phase loop is similarly

*V*), or average group velocity from the source to the receiver is simply

*V*=

*R/T*. Lastly, the apparent azimuth deviation is computed as

*Ω*= arctan

^{−1}(

*Q*/

*R*) where the transverse offset (

*Q*) for a phase loop is

*v*(

*z*) is the horizontal wind component transverse to the direction of propagation. Throughout this paper, all of the results are computed in the frame of reference of the receiver as opposed to the source by simply reversing the sign of the wind fields. It can be shown that this is also equivalent to integrating the Eikonal ray equations in differential form with a negative time step.

A discussion of the methodology for the estimation of the eigenrays associating a received signal with a given source is beyond the scope of the present work. Relevant, however, is the fact that for a specific eigenray the measured azimuth deviation is an apparent effect similar to that of an airplane yawing in a crosswind in order to maintain a constant bearing. The acoustic wavefront must be skewed at some angle *Ω* with respect to the great circle path in order to offset the net lateral advection from transverse wind components; in other words so that the net transverse offset at the top and bottom of the phase loop are zero. Although the total path does not deviate from the true great circle path between source and receiver, in the presence of transverse winds the wavefront can depart from the great circle path anywhere else in the phase loop. Over one range of altitudes a crosswind may push the ray off the great circle path, while at other altitudes a crosswind in the opposite direction may push the ray back onto the great circle path. Furthermore, the ray may deviate to one side of the path on the up leg and the other side of the path on the down leg. This is also an important factor that needs to be considered when signals are observed from a source at altitude such as a bolide. Care must be taken in automated and interactive DLC algorithms when applying calculated values of *Ω* to correct the array observations for apparent azimuth deviation. If topography and atmospheric range variations are included then the actual path can be even more complicated, however the overall characteristics remain the same.

The crux of solving the τp integrals accurately is the treatment of the inverse square-root singularity in the function *ψ*(*z*) at the upper limit of the domain. At any point in the domain (i.e. for any given *p*) the root is calculated by first bracketing it with a grid search and then applying Brent’s method to approximate the root to a high degree of accuracy (Press, 1989). Knowing the location of the square-root singularity *z*(*p*), Eqs. (3)–(6) can then be integrated with a Romberg method employing a modified midpoint rule that can handle inverse square-root singularities at the upper bound (Press, 1989). For all of the numerical results presented, continuous functional values for *u*(*z*), *w*(*z*), *c*(*z*), and *ζ*(*z*) are calculated by cubic spline interpolation of gridded G2S values with ∆*z* = 125 m. Note that the calculation of vertical derivatives is not required to integrate Eqs. (3)–(6). These integrals may also be evaluated for sources at altitude such as bolides by including a second term for the fractional part of the propagation phase loop where the limits of integration have been adjusted accordingly.

Two factors are relevant to current IDC DLC processing with respect to signals generated by sources well above the ground where the expected number of detectable phases can double at distant recording stations owing to the fact that a source will have both upward and downward directed acoustic components. First, current automated procedures focus on picking the onset time of the fastest infrasound arrival, and when and where closely spaced multiple arrivals exist, they tend to be averaged into a single characteristic by the parameters of the automated PMCC feature extraction algorithms. Secondly, progress has been made to demonstrate that it is possible to estimate hypocenter altitude at the level of interactive IDC analyst expert review, where manual identification of tropospheric, stratospheric, and thermospheric phases is possible; and in particular in conjunction with additional information from detections by the seismic, and auxiliary seismic components of the IMS network (Edwards and Hildebrand, 2004; Arrowsmith *et al.,* 2007; Le Pichon *et al.,* 2008a). As experience progresses, it will eventually be possible to implement these considerations into automated IDC processing, however as is the case in seismology, hypocenters depths are difficult to compute without a dense local network or specific depth phases. Automated hypocenter height estimates via infrasound will thus likely only be approximate until an IDC analyst can refine them.

*et al.,*1996; Picone

*et al.,*2002) for January 1, 2005 at 00:00 UT for a typical northern hemisphere mid-latitude station (I56US) are shown in Fig. 1. Illustrative τp calculations corresponding to these example profiles are shown in Fig. 2. These calculations are performed over all observable azimuths for elevation angles from 0° to 35°. The horizontal phase velocity (

*V*

_{θ}) of the parameter space over the domain is shown in panel A. Recall that this is only a function of the atmospheric conditions at the detector. Panel B shows a contour plot of the effective sound velocity as a function of altitude (

*z*) and backazimuth. The wintertime stratospheric wind jet near 55 km can be observed, with winds toward the detector at −90°, and away from the detector at +90°. The turning points of all incoming rays at elevation angles of 5°, 10°, and 15° are also indicated. The corresponding turning heights of the rays, over the entire domain, is shown in panel C. Two predominant ducts are present at this time and location, the thermospheric duct for all backazimuths and the eastward stratospheric duct from the wintertime stratospheric zonal wind jet. The dark blue area represents a region where the acoustic energy is immediately refracted downward toward the earth’s surface by the ambient atmospheric conditions. Panels D, E, and F show the celerity (

*V*), range (

*R*), and apparent azimuth deviation (

*Ω*) over the computational domain, respectively. A very stable and accurate result can be obtained over the entire domain, including in the vicinity of the cusp regions where fast propagation modes exist (Evers and Haak, 2007). These fast modes can be seen near the transition from the stratospheric to the thermospheric ducts for look directions to the west.

Several limitations resulting from the various approximations in the τp method such as the shortcomings of linear ray-tracing theory (Millet *et al.,* 2007), the lack of explicit range dependence (Drob *et al.,* 2003), and the influence of internal scattering by internal gravity waves (Chunchuzov, 2004; Ostashev *et al.,* 2005) are noteworthy but beyond the scope of the present discussion. With the doubling of processing capacities every few years following Moore’s Law, more complex calculations that account for range-dependent variations in the background atmosphere should be investigated and eventually implemented in automated DLC algorithms. The objective at hand is to provide geophysical insight to demonstrate that the utilization of climatological travel times in DLC algorithms is at best outdated in comparison to the possibility of calculating them in real time following from recent progress in atmospheric specification and infrasound propagation codes.

## 3 Results

*et al.,*(2003) investigated how infrasound propagation characteristics varied over the globe at a given universal time; in particular, how acoustic energy is partitioned between the troposphere, stratospheric, and thermosphere ducts. To provide some context, Fig. 3 shows the global distribution of infrasound ducting characteristics for an arbitrary time of 05/24/2006 00:00 UT. For a particular altitude level, each global map represents the fraction of acoustic energy from an isotropically radiating acoustic point source on the ground, summed over all possible propagation directions (see Drob

*et al.,*2003).

The regions where tropospheric ducting occurs are shown in the top panel. Ducting along the tropospheric jet stream can also be seen in the Southern Hemisphere. Marine inversion layers also occurred off the west coast of California and Africa, as well as near the Korean Peninsula. Stratospheric ducting (middle panel) is seen in the Northern And Southern Hemisphere mid-latitude regions but is absent in the equatorial regions. The lower panel shows the remaining thermospheric ducting fractions. Interesting correlations in the thermospheric ducting fractions with continental landmasses and lower atmospheric ducting fractions can also be seen. The inverse correlations between the upper and lower atmospheric ducting fractions are due to the fact that what was not ducted in the lower atmosphere can be ducted in the upper mesosphere and lower thermosphere.

Following the work of Drob *et al.,* (2003), we now present several case studies based on the calculation of a multiyear time series of infrasound propagation characteristics for two of the IMS infrasound stations; I56US a mid-latitude Northern Hemisphere station at (48.26°N, 117.13°W), and I55US a polar latitude Southern Hemisphere station at (77.74°S, 167.58°E). We compare and contrast the results calculated from both climatology (HWM93/MSISE-00) and hybrid G2S specifications. For these two IMS stations, we present a five-year long-time series from September 13, 2002 to April 30, 2007 at 6 h intervals (4× daily) of the infrasound ducting characteristics of ray turning heights z(*p*), celerity (*V*) and backazimuth (*Ω*). The later two have direct application in infrasound DLC algorithms.

In the detection algorithms described by Brown *et al.,* (2002a) currently in use at the IDC, backazimuths receive a slightly greater statistical emphasis (1.0) as compared to travel times (0.8) in the calculation of a metric (Σ) for the trigging of an automatic event (Σ > 3.55) and Reviewed Event Bulletin (REB) (Σ > 4.6). This detection criteria effectively defines a significant event as one that can be established by at least two well-defined and intersecting back azimuths for which the associated travel times do not also violate causality (Brown *et al.,* 2002a). More recently, a novel detection scheme was developed by Arrowsmith *et al.,* (2008) that dynamically adjusts network detection thresholds in real time to account for the presence of correlated and varying background noise. Furthermore, Arrowsmith *et al.,* (2008) demonstrated that the new algorithm has excellent performance characteristics in the presence of clutter, suggesting the approach provides a viable means to reduce the number of false alarms that need to be reviewed by a human analysis. Neither approach currently accounts for the hourly, daily, or seasonal changes of the travel time or azimuth deviation resulting from the corresponding changes in the atmospheric conditions; the inclusion of which would further allow for a more accurate calculation of the Σ metric thus improving the network sensitivity and reducing the number of false alarms.

## 4 I56US

*et al.,*(1998). Figure 5b shows the azimuth deviation for southward arrivals with excursions up to 10° in January 2003, and on average up to 7.5° during wintertime. In addition, there is an asymmetry with respect to the summer months with deviations of up to −3°, which tend to be more stable. These wide ranging azimuth deviations result from the annual variations of the stratospheric wind jet which is predominantly eastward, lower, stronger, and variable in the wintertime, as compared to the summertime jet which is westward, higher, and stable.

Figure 6a shows a time series of celerity for I56US for eastward arrivals again at 5° elevation, calculated with hybrid G2S and empirical atmospheric specifications. A band of arrivals at 340 m/s, which are comprised of both lower tropospheric, upper tropospheric, and even stratospheric modes, is evident. Random departures of up to 30 m/s from climatological estimates and seasonal variations occur during wintertime for the other branch of arrivals between 250 and 320 m/s.

Figure 6c shows the results for westward arrivals. Of note is the presence of occasional tropospheric arrivals (340 m/s) with clear seasonal variability. If not properly accounted for (i.e. given the appropriate statistical weighting) these could result in spurious associations and poor source localizations. The results also show that there is pronounced annual variability with stable stratospheric modes in the summer time, transitioning to thermospheric modes in the wintertime as was shown in Fig. 4. The existence of sporadic stratospheric modes occurring in both the eastward and westward directions in late winter are associated with the dynamical instability of the stratospheric wind jet driven by vertically propagating planetary waves. Disturbances associated with sudden stratospheric warmings (Manney *et al.,* 2008) can even result in prolonged intervals of westward winds in the stratosphere during the wintertime.

## 5 I55US

## 6 Discussion/Conclusion

As described in Brown *et al.,* (2002a) one could imagine tables of statistical propagation characteristics comprised of several dominant modes that could be implemented in operational DLC algorithms; a constant phase at 310–340 m/s and an annual varying one with stratospheric and thermospheric phases. In future IDC software updates, these could and should also be a function of day of the year, look direction, and station. Histogram analysis could be used to establish preferred propagation modes with uncertainties and assigned probabilities based on half-widths; however, direct utilization of the procedures we have outlined here on a daily basis is just as easy to implement. At present the IDC uses travel-time tables which are independent of season, though do depend on the elevation of arrival.

Furthermore, from the consideration of the variability of backazimuth and celerity presented, it is clear that the current seasonal averaged travel-time tables provide a poor representation of the day-to-day and month-to-month variations, and thus limit the full potential of the CTBTO automated infrasound DLC algorithms. The inherent variability is simply lost in the histogram analysis. It should be noted that in concert with the other monitoring technologies of the CTBTO, the current infrasound algorithms are passable, but improvable, as has been demonstrated by numerous researchers and results. Additional work, following examples such as Arrowsmith *et al.,* (2008); Le Pichon *et al.,* (2008c) should be undertaken in order to ascertain the value added to the system in terms of false alarm rates and network detection thresholds with careful consideration of the computational complexity and burden introduced into the existing operational system.

With respect to caveats for the calculations presented here, for certain locations and times the dynamical variability of the upper mesospheric and lower thermospheric modes may be even greater in reality than calculated here after accounting for observed and documented non-migrating tides (Forbes *et al.,* 2003), day-to-day and inter-seasonal tidal variability (Fritts and Isler, 1994; Lieberman *et al.,* 2007), and the existence of vertically propagating and stationary mesosphere lower thermosphere planetary waves (Smith, 1996; McLandress *et al.,* 2006) above 55 km. These effects are not yet fully included in either the empirical climatology or hybrid G2S atmospheric specification. The HWM93 model is also known to underestimate the magnitude of the migrating tides for certain seasons and latitudes. A recent update of HWM (HWM07) by Drob *et al.,* (2008) resolves most of the issues related to the amplitude and phases of the migrating solar tides in the mesosphere and lower thermosphere. Given a proper statistical treatment of the present uncertainties, limitations of the present atmospheric specifications above 55 km should not invalidate the applicability of the work described here to DLC algorithms. In particular, tropospheric and stratospheric modes, which have a much greater signal to noise ratio are more likely to be detected and not subject to these problems.

The τp and G2S software which produced the results presented here are specifically designed to be utilized at the IDC in batch mode via a shell script in order to compute the local propagation characteristics for all IMS infrasound stations in real time. These codes can also be invoked interactively by an IDC analysist. For a given station and time the τp calculations only require a few seconds to complete. The process is relatively fast compared to the periodic calculations of the global G2S coefficient set from available atmospheric data sources, requiring several minutes to downloading available global weather fields and perform the vector spherical harmonic transforms. With the addition or allocation of a single dedicated compute node that is accessible to the operational DLC system, the travel-time characteristics for all sixty IMS infrasound stations could be updated every 60 min. Compared to automated DLC calculations from climatological travel-time tables gains in system performance could thus be achieved.

Recent ground-truth events investigated by the infrasound research community have clearly demonstrated that accurate atmospheric specifications are required to properly explain observed infrasound signals. In tandem, the atmospheric science community is continually improving and currently producing reliable specifications of the atmospheric state that can be utilized to improve automated DLC algorithms. Given the advances and availability of low-cost computing resources, and the reliable openly available real-time atmospheric specifications such as provided by NOAA and ECMWF there are no good reasons, technical or otherwise, why near-real-time travel-time tables should not be used in infrasound propagation calculations. Of course when these systems are brought online it is important to continually monitor and evaluate the performance with the many naturally occurring geophysical, as well as coincidental man-made, ground-truth events. One possibility as already demonstrated by similar research is the example of the analysis of the multi-year time series of volcanic observations at I22FR (Le Pichon *et al.,* 2005). Lastly for robust event location and screening of automated event bulletins by human analysts (Brown *et al.,* 2002a), we recommend that detailed propagation modeling techniques that account for range dependence (Gossard and Hooke, 1975), topography (Arrowsmith *et al.,* 2007), and other effects such as interval gravity waves (Ostashev *et al.,* 2005; Chunchuzov, 2004) be utilized.

This paper has presented time series of infrasound propagation characteristics. A number of physical approximations where made to keep these calculations simple and robust. Through these calculations, we have argued that precomputed monthly average travel-time tables are poor for operational DLC algorithms. To this end, we have advanced progress toward the integration of real-time infrasound propagation travel-time tables into automated IMS processing.

## Notes

### Acknowledgments

The methodologies and tools presented here were developed in part in an effort supported by the Office of Naval Research to investigate whether signals from infrasound ground-truth events could be inverted to obtain information about the atmosphere, i.e., ground-to-space infrasound acoustic tomography, such as is currently in routine use in oceanography and seismology.

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